A 1.01mol sample of nitrogen gas is stored in a 76.1mL container at 48.1°C. Calculate the pressure exerted by nitrogen gas in the container. Be sure your answer has the correct number of significant figures.
Question
A 1.01mol sample of nitrogen gas is stored in a 76.1mL container at 48.1°C. Calculate the pressure exerted by nitrogen gas in the container. Be sure your answer has the correct number of significant figures.
Solution
To solve this problem, we will use the ideal gas law equation: PV = nRT
Where: P = pressure V = volume n = number of moles R = ideal gas constant T = temperature in Kelvin
First, we need to convert the volume from mL to L because the ideal gas constant R is usually given in L·atm/(K·mol).
76.1 mL = 0.0761 L
Next, we need to convert the temperature from Celsius to Kelvin because the ideal gas law requires the temperature to be in Kelvin.
T(K) = T(°C) + 273.15 T = 48.1°C + 273.15 = 321.25 K
Now we can substitute the values into the ideal gas law equation. The value of R is 0.0821 L·atm/(K·mol).
P = nRT / V P = (1.01 mol * 0.0821 L·atm/(K·mol) * 321.25 K) / 0.0761 L
Now, calculate the above expression to find the pressure.
P = 34.5 atm
So, the pressure exerted by the nitrogen gas in the container is 34.5 atm.
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